Answer:
x has to be 6
Step-by-step explanation:
Let us revise the rule of the area of a triangle
→ The area of any triangle = [tex]\frac{1}{2}[/tex] × base × height
In the given triangle:
∵ The triangle is a right triangle
∵ Its base = 5x ft
∵ Its height = 12 ft
∵ Its area = 180 ft²
→ Substitute these values in the rule of the area above
∴ 180 = [tex]\frac{1}{2}[/tex] × 5x × 12
→ Simplify the right side
∵ [tex]\frac{1}{2}[/tex] × 5x × 12 = 30x
∴ 180 = 30x
→ Divide both sides by 30 to find x
∴ [tex]\frac{180}{30}=\frac{30x}{30}[/tex]
∴ 6 = x
∴ x has to be 6
To check your answer find the area of the triangle
∵ Its base = 5x = 5(6) = 30 ft
∵ Its height = 12 ft
∴ Its area = [tex]\frac{1}{2}[/tex] × 30 × 12 180 ft²
∴ The value of x is correct.
