Based on the information below, is ? Explain. RS = x2 + 4x – 21, RT = x2 + 5x – 24, ST = x2 + 9x – 36 AB = x + 7, AC = x + 8, BC = x + 9

Question

is triangle RST congruent to Triangle ABC

Answer 1

x² + 4x – 21 = (x – 3)(x + 7)
x² + 5x – 24 = (x – 3)(x + 8)
x² + 9x – 36 = (x – 3)(x + 12) 

Last one is not matched with BC, therefore triangles are not congruent

Answer 2

Hey Tanner -- looks like an (x-3) factor relates 2 of the sides, but not the BC segment ... Regards, sir :)

Answer 3

For the two triangles to be congruent, all corresponding sides must be equal.  In other words, side RS in the first triangle must equal side AB in the second triangle, side RT must equal side AC, and side ST must equal side BC.

From the info provided, for RS to equal AB, x²+4x-21 must equal x+7.  We can solve for x, as follows:

X²+4x-21=x+7

X²+4x-x-21-7=0

x²+3x-28=0

Factoring we get  (x+7)(x-4)=0

Solving for x, we get x=-7 or x=4;  -7 can be ruled out as the length of a side, since it's negative.

Therefore, RS is equal to AB, only when x=4.

 

Similarly, for side RT to equal side AC, x²+5x-24 must equal x+8;

x²+5x-x-24-8=0

x²+4x-32=0

(x-4)(x+8)=0

x=4 or x=-8; We can rule out -8.

So, RT is equal to AC, only when x=4.

So far, with x=4, the first two corresponding sides are equal.

 

If we now plug 4 in for the value of x in the third corresponding sides ST and BC, we get:

ST=x²+9x-36=4²+(9)(4)-36=16

BC=x+9=4+9=13

Since 16 is not equal to 13, ST is not equal to BC and the triangles are not congruent.