Answered

Makakuha ng detalyadong mga sagot sa iyong mga tanong gamit ang IDNStudy.com. Tuklasin ang malalim na sagot sa iyong mga tanong mula sa aming komunidad ng mga bihasang propesyonal.

A figure is composed of four congruent right triangles.
If the area of the large square is 13 square units, the area of the small square in
the middle part is 1 square unit, then what is the sum of the cubes of the two legs of each right triangle?

A Figure Is Composed Of Four Congruent Right Triangles If The Area Of The Large Square Is 13 Square Units The Area Of The Small Square In The Middle Part Is 1 S class=

Sagot :

Nzmidn

SOLUTION:

Let x and y be the two legs of each right triangle.

As shown in the figure, the area of the small square in the middle part is 1 square unit, and the area of the large square is 13 square units.

Thus, the sum of the four congruent right triangles is 13 - 1 = 12 square units.

Now, add a right triangle with same area to the outside of each right triangle such that this forms another larger square.

Hence, the area of the larger square is 13 + 12 = 25 square units.

This implies that the side of the square is 5 units as s² = Area.

Moreover, we can observe that the sum of the two legs of the right triangle is equal to the side length of the largest square, which is 5 units.

Also, the difference between the two legs is exactly equal to the side length of the original square; that is 1 unit.

So,

[tex]\begin{cases} \sf x + y = 5\\ \sf x - y = 1\\\end{cases}[/tex]

Adding the two equations and solving, we get (x,y) = (3,2).

Therefore, the sum of the cubes of the two legs of each right triangle is

3³ + 2³ = 35 units

ANSWER:

35 units.

#skwrijwrijqaspqrnwqwz

Salamat sa iyong kontribusyon. Huwag kalimutang bumalik upang magtanong at matuto ng mga bagong bagay. Ang iyong kaalaman ay napakahalaga sa ating komunidad. Salamat sa pagbisita sa IDNStudy.com. Bumalik ka ulit para sa mga sagot sa iyong mga katanungan.