The height of a triangle is 2cm less than its width. the area of the triangle is 24cm squared. what are the measures of the base and height? plz answer asap!

The measure of the base is 8 cm and the measure of the height is 6 cm and this can be determined by using the formula of the area of the triangle.

Given :

The following steps can be used in order to determine the measures of the base and height:

Step 1 - The formula of the area of the triangle can be used in order to determine the measures of the base and height.

Step 2 - The area of a triangle is given below:

  --- (1)

where B is the base and H is the height of the triangle.

Step 3 - According to the given data, the height of a triangle is 2cm less than its width that is base.

H = B - 2

Step 4 - Substitute the value of B and A in the expression (1).

Step 5 - Simplify the above expression.

Step 6 - Factorize the above quadratic equation.

B(B - 8) + 6(B - 8) = 0

(B + 6)(B - 8) = 0

B = 8 cm

Step 7 - So, the measure of height is:

H = 8 - 2

H = 6 cm

For more information, refer to the link given below:

link

Triangle height = base -2

Triangle Area = .5 base * height

24 cm² = .5base * (base -2)

24 cm² = .5base² - base

.5 base² -base - 24 = 0

Solving with quadratic formula base = 8 and height = 6

Double - Check

Area = .5 * 8 * 6 = 24

Step-by-step explanation:

step-by-step explanation: yes