$\displaystyle A=\frac{1}{2}bh$. 

$\displaystyle 6x=42$

$\displaystyle x=7$

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle 2x-2$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+2x-2=22$

$\displaystyle 4x-2=22$

$\displaystyle 4x=24$

$\displaystyle x=6$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=2(6)-2=10$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{6^2-5^2}=\sqrt{11}=3.32$

Make sure to round to $\displaystyle 2$ places after the decimal.

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle 3x-18$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+3x-18=32$

$\displaystyle 5x-18=32$

$\displaystyle 5x=50$

$\displaystyle x=10$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=3(10)-18=12$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{10^2-6^2}=\sqrt{64}=8$

Make sure to round to $\displaystyle 2$ places after the decimal.

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle 2x-1$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+2x-1=19$

$\displaystyle 4x-1=19$

$\displaystyle 4x=20$

$\displaystyle x=5$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=2(5)-1=9$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{5^2-4.5^2}=\sqrt{4.75}=2.18$

Make sure to round to $\displaystyle 2$ places after the decimal.

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle 3x-14$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+3x-14=16$

$\displaystyle 5x-14=16$

$\displaystyle 5x=30$

$\displaystyle x=6$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=3(6)-14=4$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{6^2-2^2}=\sqrt{32}=5.66$

Make sure to round to $\displaystyle 2$ places after the decimal.

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle \frac{1}{3}x-2$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+\frac{1}{3}x-2=19$

$\displaystyle \frac{7}{3}x-2=19$

$\displaystyle \frac{7}{3}x=21$

$\displaystyle x=9$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=\frac{1}{3}(9)-2=1$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{9^2-(\frac{1}{2})^2}=\sqrt{80.75}=8.99$

Make sure to round to $\displaystyle 2$ places after the decimal.

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle 2x-10$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+2x-10=38$

$\displaystyle 4x-10=38$

$\displaystyle 4x=48$

$\displaystyle x=12$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=2(12)-10=14$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{12^2-7^2}=\sqrt{95}=9.75$

Make sure to round to $\displaystyle 2$ places after the decimal.

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle \frac{1}{3}x+4$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+\frac{1}{3}x+4=11$

$\displaystyle \frac{7}{3}x+4=11$

$\displaystyle \frac{7}{3}x=7$

$\displaystyle x=3$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=\frac{1}{3}(3)+4=5$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{3^2-(\frac{5}{2})^2}=\sqrt{2.75}=1.66$

Make sure to round to $\displaystyle 2$ places after the decimal.

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle \frac{1}{4}x+5$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+\frac{1}{4}x+5=50$

$\displaystyle \frac{9}{4}x+5=50$

$\displaystyle \frac{9}{4}x=45$

$\displaystyle x=20$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=\frac{1}{4}(20)+5=10$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{20^2-5^2}=\sqrt{375}=19.36$

Make sure to round to $\displaystyle 2$ places after the decimal.

First, find the lengths of the triangle.

Let $\displaystyle x$ be the length of each leg. Then, the length of the base must be $\displaystyle \frac{1}{8}x+10$.

Use the information given about the perimeter to solve for $\displaystyle x$.

$\displaystyle x+x+\frac{1}{8}x+10=44$

$\displaystyle \frac{17}{8}x+10=44$

$\displaystyle \frac{17}{8}x=34$

$\displaystyle x=16$

Plug this value in to find the length of the base.

$\displaystyle \text{Length of Base}=\frac{1}{8}(16)+10=12$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\displaystyle \text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\displaystyle \text{Height}=\sqrt{16^2-6^2}=\sqrt{220}=14.83$

Make sure to round to $\displaystyle 2$ places after the decimal.