Question

1. the area of a triangle is 52 square centimeters. if the base of the triangle is 13 centimeters, find its height.
2. an equilateral triangle has an area of 97.5 square meters. if the height of the triangle is 13 meters, find the perimeter of the triangle.

Explanation:

Question 14

Step1: Recall the area formula of a triangle

The area formula of a triangle is $A=\frac{1}{2} \times b \times h$, where $A$ is the area, $b$ is the base, and $h$ is the height.

Step2: Substitute the known values into the formula

We know that $A = 52$ square centimeters and $b = 13$ centimeters. Substitute these values into the formula: $52=\frac{1}{2} \times 13 \times h$.

Step3: Solve for $h$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times13\times h=\frac{13h}{2}$. Then we have the equation $\frac{13h}{2}=52$. Multiply both sides of the equation by 2 to get $13h = 52\times2=104$. Then divide both sides by 13: $h=\frac{104}{13} = 8$.

Step1: Recall the area formula of a triangle

The area formula of a triangle is $A=\frac{1}{2}\times b\times h$, where $A$ is the area, $b$ is the base, and $h$ is the height.

Step2: Substitute the known values to find the base

We know that $A = 97.5$ square meters and $h = 13$ meters. Substitute these values into the formula: $97.5=\frac{1}{2}\times b\times13$. First, simplify the right - hand side: $\frac{1}{2}\times13\times b=\frac{13b}{2}$. Then we have the equation $\frac{13b}{2}=97.5$. Multiply both sides by 2: $13b=97.5\times2 = 195$. Divide both sides by 13: $b=\frac{195}{13}=15$ meters.

Step3: Calculate the perimeter of the equilateral triangle

Since the triangle is equilateral, all sides are equal. The perimeter $P$ of an equilateral triangle with side length $b$ is $P = 3b$. Substitute $b = 15$ meters into the formula: $P=3\times15 = 45$ meters.

Answer:

The height of the triangle is 8 centimeters.

Question 16