Question

Beth draws triangle PQR, she also draws a square with side length PQ, a square with side length QR, and a square with side length RP.

Answer 1

Beth's statement is true always in the case of the right triangle i.e.option (A)

Given a triangle PQR and squares of side's PQ, QR and RP and beth state's that sum of the area of two squares is equal to the area of the third square and asked which triangle justifies the statement.

Assume the triangle PQR with side lengths PQ=X, QR=Y, and RP=Z

and squares of side's PQ(X), QR(Y) and RP(Z) [image attached]      

According to the given statement

area of square=$(length of side)^{2}$

$X^{2} +Y^{2} =Z^{2}$ ( i.e. the sum of areas of two squares equal to the area of third square)

The about equation matches with Pythagorean theorem

Pythagorean theorem:

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle, according to Pythagoras' theorem.

As the Pythagorean theorem is applicable for right triangle

so,the type of triangle is right triangle.i.e.option(A)

Learn more about right triangle here:

brainly.com/question/6322314

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