On a coordinate plane, a straight line with a negative slope, labeled f of x, crosses the y-axis at (0, 4), and the x-axis at (4
2 answers:
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Answer:
Option d. PQ = YZ
Step-by-step explanation:
<u><em>The question in English is</em></u>
Choose the most appropriate answer. The PQR triangle and the XYZ triangle are two congruent triangles. The angle P = the angle Y and PR = YX. Side pairs of the same length are ... a. PQ = XZ b. QR = YZ c. QR = XY d. PQ = YZ
we know that
If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent
Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement
so
we have that
so
Triangle PQR is congruent with Triangle YZX
That means
<em><u>Corresponding angles</u></em>
<u><em>Corresponding sides</em></u>
Let us assume uniform width = x cm wide.
Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.
Therefore, length of rectangle made by frame = 50 + x+x = (2x+50) cm.
And width of rectangle made by frame = 70+x+x = (2x+70) cm.
We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.
Total area of the rectangle made by frame would be = (2x+50) * (2x+70)
We know,
Actual area of frame = Area of rectangle made by frame - area of rectangular portrait.
We also given "the area of the frame is the same as the area of the portrait."
We can setup an equation now,
3500 = (2x+50) * (2x+70) - 3500.
Subtracting 3500 from both sides, we get
3500-3500 = (2x+50) * (2x+70) - 3500-3500.
0 = (2x+50) * (2x+70) -7000.
FOIL (2x+50) * (2x+70), we get
0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.
0 = 4x^2 +140x +100x +3500 -7000.
4x^2 +240x -3500 = 0.
Dividing whole equation by 4, we get
x^2 +60x - 875 =0
Applying quadratic formula , we get
We cant take negative value.
So,
We could take approximately 12 cm.