Question

What is the numerical length of 19x - 36?

Answer 1

Answer: 230

Explanation:

Because the midline that intersects the triangle is the midpoint of both the sides. We know this because the midline breaks the sides in half. When this happens, the midline is half the base. Or the base is 2 times as long as the midline.

To write an equation. you need to multiply midline by 2 to make it equal to the base.

19x-36 = 2(6x +31) >Distribute

19x -36 = 12x +62 >Bring like terms to same side

7x = 98

x = 14 >Not done. We need to substitute back into base.

19x - 36 >Substitute x into base

=19(14) -36

=230

Answer 2

`\textsf{The numerical length of 19x - 36 is }\bold{\underline{ 230.}}`

Explanation:

Given:

Let's answer this question by naming it.

Figure: Attachment

Iet big triangle be ABC and Small triangle be ADE.

Given:

DE = 6x + 31

BC = 19x - 36

To find : BC = 19x - 36

AE = EC

AD = DB

so,

AC = 2AE

AB = 2AD

It means the corresponding side ratio are:

`\sf (AE )/(AC) = (AE)/(2 AE) = (1)/(2)`

`\sf (AD )/(DB) = (AD)/(2 AD) = (1)/(2)`

Since the corresponding side's ratio is equal. it means,

ΔADE is similar to ΔABC.

As we know that,
corresponding side ratio of similar triangle are proportional, so

`\sf (DE )/(BC) = (1)/(2)`

Substituting value of DE and BC

`\sf (6x+31)/(19x-36) = (1)/(2)`

Doing Criss cross multiplication:

`\sf 2(6x+31) = 19x -36`

Opening bracket

`\sf 12x + 62 = 19 x -36`

Adding 36 and subtracting 12x on both sides

`\sf 12x + 62 +36 - 12 x = 19x-36+36-12x`

`\sf 98 = 7 x`

Dividing both side by 7, we get

`\sf x = (98)/(7)`

`\sf x = 14`

Now,

BC = 19x - 36 = 19*14 -36 =230

Therefore, The numerical length of 19x - 36 is 230.