What number needs to be added to both sides of the equation in order to complete the square?

Mathematics

2 answers:

IRISSAK [1]2 years ago

8 0

Answer:

Step-by-step explanation:

The formula for the whole square is

$\left ( a+b \right )^2=a^{2}+2ab+b^{2}$

So, to make the complete square, in the expression

$x^{2}+14x = - 32$

First take half of the term 14 x that is 7x and then divide it by x so it is 7. Now take its square that is 49. So add 49 on both the sides to make the given expression as a whole square.

Sever21 [200]2 years ago

5 0

x^2+14x = (x+7)^2

7^2 = 49

so you would add 49 to both sides

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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

Nutka1998 [239]

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

$11x+16x+24x = 51x$ feet long. But we know that this is 510 feet, so we have

$51x = 510 \implies x = \cfrac{510}{51} = 10$ .

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 $s$ is half the perimeter of the triangle whose sides are $a,b,c$ , the area $A$ is given by