Question

A triangle has a base of 7 feet and a height of 10 feet. By how much does the height need to increase for the area to increase by 10.5 square feet? Write your answer as a decimal.

Answer 1

Area of a triangle = 1/2 x base x height

Area of original triangle = 1/2 x 7 x 10 = 35 square feet.

Add 1.5 feet to area to get 35 + 10.5 = 45.5 square feet.

Solve for the new height:

45.5 = 1/2 x 7 x H

Multiply both sides by 2:

91 = 7 x H

Divide both sides by 7:

H = 91/7

H = 13 feet

The new height needs to be 13 feet.

13 - 10 = 3 feet

The height has to increase by 3 feet.