Question

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!

Answer 1

Answer:

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:

Answer 2

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 height of a triangle is 2 cm less than its base.
• The area of the triangle is 24 cm squared.

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:

$\rm A= \dfrac{1}{2}\times B \times H$   --- (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).

$\rm 24= \dfrac{1}{2}\times B \times (B-2)$

Step 5 - Simplify the above expression.

$\rm 48 = B(B-2)$

$\rm B^2-2B -48=0$

Step 6 - Factorize the above quadratic equation.

$\rm B^2-8B+6B-48=0$

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:

https://brainly.com/question/16171588