Asquare hot tub will be placed in the center of an enclosed area near the pool. each side of the hot tub measures 6 feet. it will be surrounded by x feet of deck on each side. the enclosed space is also square and has an area of 169 square feet. find the width o the deck space around the hot tub, x. part 1 write an equation for the area of the enclosed space in the form y=(side length)^2. hint: don't forget to add x to each side of the hot tub. part 2 substitute the area of the enclosed space for y in your equation. part 3 solve your equation from part 2 for x. part 4 what is the width of the deck around the hot tub.

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)