# Simplify an expression for the perimeter of the rectangle shown.
8.6x + 3

5.2

4

Write your answer with NO spaces:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in [tex]\delta bea[/tex] and [tex]\delta dea[/tex];

[tex]ba=da[/tex], as these are radii of our given circle.

[tex]ea=ea[/tex]

therefore, [tex]\delta bea\cong \delta dea[/tex] by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

[tex]3x-24=x+10[/tex]

[tex]3x-x=24+10[/tex]

[tex]2x=34[/tex]

[tex]x=\frac{34}{2}[/tex]

[tex]x=17[/tex]

now let us substitute x=17 in the expression for the length of be.

[tex]\text{length of be}=3x-24[/tex]

[tex]\text{length of be}=3\cdot 17-24[/tex]

[tex]\text{length of be}=51-24[/tex]

[tex]\text{length of be}=27[/tex]

therefore, length of be will be 27 units and option c is the correct choice.

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