Question

An isosceles triangle has an area of 175 ft^2. If the base is 16 ft, what is the length of each leg? Round the answer to the nearest tenth.

Answer 1

A=bh/2

h=2A/b

h=2*175/16

h=21.875

h^2=s^2-(b/2)^2

h^2=s^2-b^2/4

h^2=(4s^2-b^2)/4

4h^2=4s^2-b^2

4s^2=4h^2+b^2

s^2=(4h^2+b^2)/4

s=√((4h^2+b^2)/4), since h=21.875 and b=16

s=√542.515625

s≈23.3 ft

Answer 2

The length of each leg of the isosceles triangle is 23.3 ft

Calculating length

From the question, we are calculate the length of the each leg of the isosceles triangle

First, we will calculate the height of the triangle

Using the formula for calculating the area of a triangle

$A = \frac{1}{2} bh$

Where A is the area

b is the base

and h is the height

From the given information,

A = 175 ft²

b = 16ft

∴ $175 = \frac{1}{2} \times 16 \times h$

175 = 8h

h = 21.875 ft

Let l represent the length of a leg of the triangle,

By Pythagoras' theorem,

l² = h² + 8²

∴ l² = 21.875² + 64

l² = 478.515625 + 64

l² = 542.515625

l = √542.515625

l = 23.29196

l ≅ 23.3 ft

Hence, the length of each leg of the isosceles triangle is 23.3 ft

Learn more on Calculating area of triangle here: https://brainly.com/question/16294004

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