Question

use the information about the figure to find the indicated measure. 23. area = 504 in.² find the height h. 24. area = 55.5 m² find the base b. 25. perimeter = 112.5 m find the length ℓ.

Explanation:

Problem 23:

Step1: Recall triangle area formula

The area \( A \) of a right triangle is given by \( A=\frac{1}{2}\times\text{base}\times\text{height} \). Here, \( A = 504\space\text{in}^2 \) and base \( = 42\space\text{in} \), height \( = h \). So the formula becomes \( 504=\frac{1}{2}\times42\times h \).

Step2: Simplify and solve for \( h \)

First, simplify \( \frac{1}{2}\times42 = 21 \). So the equation is \( 504 = 21h \). Then, divide both sides by 21: \( h=\frac{504}{21} \).

Step3: Calculate the value

\( \frac{504}{21}=24 \).

Step1: Recall triangle area formula

The area \( A \) of a triangle is \( A = \frac{1}{2}\times\text{base}\times\text{height} \). Here, \( A=55.5\space\text{m}^2 \), height \( = 9.25\space\text{m} \), base \( = b \). So \( 55.5=\frac{1}{2}\times b\times9.25 \).

Step2: Simplify and solve for \( b \)

First, multiply both sides by 2: \( 55.5\times2=b\times9.25 \), which gives \( 111 = 9.25b \). Then, divide both sides by 9.25: \( b=\frac{111}{9.25} \).

Step3: Calculate the value

\( \frac{111}{9.25}=12 \).

Step1: Recall rectangle perimeter formula

The perimeter \( P \) of a rectangle is \( P = 2\times(\text{length}+\text{width}) \). Here, \( P = 112.5\space\text{m} \), width \( = 12.5\space\text{m} \), length \( = l \). So \( 112.5=2\times(l + 12.5) \).

Step2: Simplify and solve for \( l \)

First, divide both sides by 2: \( \frac{112.5}{2}=l + 12.5 \), which is \( 56.25=l + 12.5 \). Then, subtract 12.5 from both sides: \( l=56.25 - 12.5 \).

Step3: Calculate the value

\( 56.25-12.5 = 43.75 \).

Answer:

The height \( h \) is \( 24\space\text{in} \).

Problem 24: