The perimeter of a triangle is 510 feet and the sides are in the ratio of 11: 16: 24. find the area of the triangle

If the sides are in the ratio of 11:16:24, it means that they are all multiples of a same number x, according to these factors.

So, the shorter side is 11x feet long, the middle one is 16x feet long, and the longest side is 24x feet long.

This means that the perimeter is

feet long. But we know that this is 510 feet, so we have

.

So, the three sides are 110, 160 and 240 feet long.

To find the area of a triangle knowing its three sides, you can use Heron's formula, which states that, if is half the perimeter of the triangle whose sides are , the area is given by

In our case, so the formula becomes

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.