Answer:
The value of BK is 3m and the value of CK is 2.4m.
Step-by-step explanation:
Given information: ABCD trapezoid
, BC=1.2m, AD=1.8m
, AB=1.5m, CD=1.2m
, AB∩CD=K.
Using the given information draw a figure.
Two sides of a trapezoid are parallel.
Since AB∩CD=K, therefore AB and CD are not parallel, because parallel line never intersect.
[tex]AD\parallelBC[/tex]
[tex]\angle KBC=\angle KAD[/tex] (Corresponding angles)
[tex]\angle KCB=\angle KDA[/tex] (Corresponding angles)
By AA rule of similarity
[tex]\triangle KBC\sim \triangle KAD[/tex]
Corresponding sides of similar triangles are proportional.
[tex]\frac{KB}{KA}=\frac{KC}{KD}=\frac{BC}{AD}[/tex]
[tex]\frac{x}{x+1.5}=\frac{y}{y+1.2}=\frac{1.2}{1.8}[/tex]
[tex]\frac{x}{x+1.5}=\frac{1.2}{1.8}[/tex]
[tex]\frac{x}{x+1.5}=\frac{2}{3}[/tex]
[tex]3x=2x+3[/tex]
[tex]x=3[/tex]
The length of BK is 3 m.
[tex]\frac{y}{y+1.2}=\frac{1.2}{1.8}[/tex]
[tex]\frac{y}{y+1.2}=\frac{2}{3}[/tex]
[tex]3y=2y+2.4[/tex]
[tex]y=2.4[/tex]
The length of CK is 2.4 m.
ΔAKD is similar to the ΔBKC. Then the ratio of the corresponding sides will remain constant. Then the value of BK and CK is 3 and 2.4 respectively.
Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
The dimension of the figure.
ABCD trapezoid
BC=1.2m, AD=1.8m
AB=1.5m, CD=1.2m
AB∩CD=K
Let x be BK and y be CK.
ΔAKD is similar to the ΔBKC. Then the ratio of the corresponding sides will remain constant. That is given as
[tex]\rm \dfrac{KB}{KA} = \dfrac{KC}{KD} = \dfrac{1.2}{1.8}[/tex]
That can be written as
[tex]\rm \dfrac{x}{x+1.5} = \dfrac{y}{y+1.2} = \dfrac{1.2}{1.8}[/tex]
From first and third, we have
[tex]\begin{aligned} \dfrac{x}{x+1.5} &= \dfrac{1.2}{1.8}\\\\\dfrac{x}{x+1.5} &= \dfrac{2}{3}\\\\3x &= 2x + 3\\\\x &= 3 \end{aligned}[/tex]
For the last two-term, we have
[tex]\begin{aligned} \dfrac{y}{y+1.2} &= \dfrac{1.2}{1.8}\\\\\dfrac{y}{y+1.2} &= \dfrac{2}{3}\\\\3y &= 2y + 2.4\\\\y &= 2.4 \end{aligned}[/tex]
Thus, the value of BK and CK is 3 and 2.4 respectively.
More about the triangle link is given below.
https://brainly.com/question/25813512
