# calculateWhat is the length of the base of a triangle with height 7 m and area 15 3/4 m2?

hala718 | Certified Educator

Let us assume that ABC is a right angle triangle where AC is the hypotenuse, BC is the base, and AB is the height.

Given the height of the triangle is 7 m and the area is 15 3/4.

==> AB = 7

We need tof find the base (BC).

We know that the formula for the area of a triangle is given by:

A = (1/2)* base * height

==> A = (1/2)* BC * AB

==> 15 3/4 = (1/2) * BC * 7

==> 63/4 = (1/2) * BC * 7

We will mutiply by 2/7

==> (2/7)*(63/4) = BC

==> BC = 9/2 = 4 1/2

Then the length of the base is 4 1/2

giorgiana1976 | Student

Since there are given the base and the height values, we'll apply the most common formula for an area of the triangle:

S = base*height/2

base  = x and

height = 7  m

the Area = 15 3/4 = 63/4 m^2

63/4 m^2 = (x*7)/2

2*63/4 = 7x

We'll simplify and we'll get:

63/2 = 7x m

x = 63/14

x = 4.5 m

So, the length of the base of a triangle with height 7 m and area 15 3/4 m^2 is x = 4.5 m.