Question

find the unknown side length.
7
10 ft
a = 25 ft²
h =
8
4 cm
a = 36 cm²
b =
9
5 in
a = 15 in²
b =

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}bh\).

Step2: Solve for \(h\) in problem 7

Given \(A = 25\space ft^{2}\) and \(b=10\space ft\). Substitute into the formula \(25=\frac{1}{2}(10)h\). First, simplify \(\frac{1}{2}(10)=5\). So the equation becomes \(25 = 5h\). Then divide both sides by 5: \(h=\frac{25}{5}=5\space ft\).

Step3: Solve for \(b\) in problem 8

Given \(A = 36\space cm^{2}\) and \(h = 4\space cm\). Substitute into the formula \(36=\frac{1}{2}(b)(4)\). First, simplify \(\frac{1}{2}(4) = 2\). So the equation becomes \(36=2b\). Then divide both sides by 2: \(b=\frac{36}{2}=18\space cm\).

Step4: Solve for \(b\) in problem 9

Given \(A = 15\space in^{2}\) and \(h = 6\space in\). Substitute into the formula \(15=\frac{1}{2}(b)(6)\). First, simplify \(\frac{1}{2}(6)=3\). So the equation becomes \(15 = 3b\). Then divide both sides by 3: \(b=\frac{15}{3}=5\space in\).

Answer:

1. \(h = 5\space ft\)
2. \(b=18\space cm\)
3. \(b = 5\space in\)