Question

30 ft

Answer 1

Answer:

32 ft

Step-by-step explanation:

find the area of the large rectangle:

30 x 16 = 480

find the area of the small rectangle:

10 x 8 = 80

subract the small rectangle from the big rectangle to get the area of the shaded region:

480 - 80 = 400

now plug this area and the height into the equation for triangle area:

A = bh/2

400 = b(25)/2 multiply both sides by 2

2(400) = 2(25b/2)

800 = 25b divide both sides by 25

800/25 = 25b/25

32 = b

Answer 2

For this case we have that the area of the shaded region is given by the subtraction of the large rectangle minus the small rectangle.

$A_ {sr} = 30 * 16-10 * 8\\A_ {sr} = 480-80\\A_ {sr} = 400$

Thus, the area of the shaded region is $400 \ ft ^ 2$

If the triangle must have the same area and a height of 25, then we have:

$400 = \frac {1} {2} b * 25\\400 = 12.5b$

Dividing between 12.5 on both sides of the equation:

$b = 32$

Thus, the base of the triangle is 32.

Answer:

32