Mathematics, 24.04.2021 04:00 mayac5369

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Answer from: FlyingUnicorn123

256 square units

Step-by-step explanation:

The area of a square is the length of one of the sides of the square squared

First square's area:

(3x+7)^2

=9x^2+42x+49

Second square's area:

(5x+1)^2

=25x^2+10x+1

The squares are the identical, so the areas are equivalent

9x^2+42x+49=25x^2+10x+1

solve for x

9x^2+42x+49=25x^2+10x+1

-16x^2+32x+48=0

use the quadratic formula

x=-1, x=3

if you substitute x for -1 for both squares' sides, the blue side comes out positive but the green square's side comes out negative, which is impossible, so we can eliminate that answer.

substituting x=3 for the sides, we get 16 as the side for both.

16^2=256

256 square units is the answer.

Answer from: Quest

The correct answer is: b

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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