Mathematics, 12.07.2019 06:00, benjamenburton1

The plans for a rectangular deck call for the width to be 4 feet less than the length. sam wants the deck to have an overall perimeter of 52 feet. what should the length of the deck be?

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Since rectangles have two pairs of equal-length sides, for any rectangle with length L and width W, its perimeter is always 2L + 2W (or 2(L + w), whichever you prefer). Here, we're told that the width is 4 feet less than the length. Symbolically, we'd say that W = L - 4. This allows us to write the perimeter entirely in terms of length if we replace our W with the expression on the right side:

2L + 2W = 2l + 2(L - 4) = 2L +2L - 8 = 4L - 8

Sam wants this expression to come out to 52, so we can set up the equality 4L - 8 = 52 and solve for L to find what the length has to be:

Adding 8 to either side, the equality becomes 4L = 60. Diving either side by 4 gives us L = 15, which tells us that the length of the deck should be 15 feet.

answered: Guest

option: d is correct

step-by-step explanation:

answered: Guest

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.